Synchronous counters — using synchronous construction, the overall propagation delay can be reduced to (approximately) the delay of what element(s)?

Introduction / Context:Counter speed is limited by cumulative propagation delay. Ripple (asynchronous) counters suffer from stage-by-stage delays. Synchronous counters clock all flip-flops simultaneously and use combinational gating to determine the next state, greatly reducing the worst-case timing path. This item asks you to identify what the effective delay reduces to in synchronous design.

Given Data / Assumptions:

• Synchronous counter architecture.
• All storage elements share the same clock edge.
• Next-state logic (gates) drives the flip-flop inputs.

Concept / Approach:In synchronous counters, the critical path typically goes through a small amount of combinational logic (for toggling conditions) into the D/T/J-K inputs of a flip-flop, then through the flip-flop itself to the outputs. Thus, the worst-case delay resembles the sum of one gating network and one flip-flop propagation delay rather than an accumulative chain of multiple flip-flops as in ripple designs.

Step-by-Step Solution:

Verification / Alternative check:Timing diagrams show outputs settling after one clock edge by an amount governed by the maximum input-combinational delay plus flip-flop Q delay, confirming the characterization.

Why Other Options Are Wrong:

• All flip-flops and gates: Describes ripple behavior, not synchronous.
• All flip-flops and gates after a 3-count: Arbitrary restriction; synchronous delay does not depend on the count value like this.
• A single gate only: Ignores flip-flop propagation delay which always exists.

Common Pitfalls:Assuming synchronous counters are “instantaneous.” Clock-to-Q and gate delays remain; they are simply not chained across stages.

Final Answer:The delay is approximately that of one gating path plus one flip-flop.